First things first: 1, how sure are you that the units are accurate and 2, how objective is your measurement of inebriation?

Let's assume that you have consumed exactly 10 units via wine on one occasion, measured your state of drunkeness (walking a line, solving problems, vision tests, whatever); and then quaffed 10 units rum-wise in the same period of time on a separate occasion, having eaten similarly beforehand etc., and then done the same tests. Sorry to be a bore, but it's the only way to get subjective factors out of the equation.

OK. The results confirm you are more drunk on wine than rum. (I'm not saying they will confirm it, but I'm going along with your data.) We have to start thinking of reasons why, and the only thing I can come up with is absorption rates. Wine is typically 13% alcohol and rum is usually 3 times stronger. Tentatively, I wonder if absorption of strong drinks is slower than more dilute drinks.

I've just googled for it and apparently there is some evidence that maximum absorption rates occur when the drink is around 20% alcohol, and that it slows with neat spirits due to irritation of the gastrointestinal surface. Beware though - you'll get just as much alcohol, but at a different rate.

10 units at a sitting is quite a chunk. Have fun!

Pete displayed his characteristic analytic and investigative bent with that answer.

A highly intelligent and trusted friend of mine told me, and I have similar anecdotal evidence from other, remoter quarters, that after a night's binge in which spirituous liquors featured lavishly, he could go to bed and wake up thirsty but reasonably sober (!?!) next morning. He then wold drink water, and very soon he would be drunk again. 

The obvious interpretation is that he had had stomach contents too concentrated to absorb rapidly, but that diluting it had drastically increased the rate of absorption. Most unfortified wines (and beers) are too dilute in the first place to prevent a reasonable rate of absorption whether one drinks water afterwards or not.

It probably would be healthier, and certainly safer, if more wasteful, to vomit it all up before absorbing much of the drink, as many uninured drinkers often do.

Mind you, there is that story Billy Connolly retailed about the couple of Glaswegians who sampled the Pope's tipple in Rome...